##  [Porous Set](/porous-set) 

  ##  [Porous Set](https://puremath.quantumdictionary.io/porous-set-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A subset E of a metric space (X,d) is porous if there exists a constant c ∈ (0,1) such that for every point x ∈ E and every sufficiently small radius r > 0 there exists a point y with the open ball B(y, c r) contained in B(x, r) bsp;\ E; intuitively E has holes of relative radius at least c at all small scales around each of its points.